Investigating the accelerated expansion of the Universe through updated constraints on viable $f(R)$ models within the Palatini formalism

TL;DR

This study evaluates seven $f(R)$ gravity models within the Palatini formalism using diverse cosmological data, demonstrating their viability as alternatives to dark energy in explaining the Universe's accelerated expansion.

Contribution

It provides updated constraints on multiple $f(R)$ models in Palatini formalism, showing their consistency with observational data and their potential to explain cosmic acceleration without dark energy.

Findings

$f(R)$ models fit observational data well

Cosmological evolution matches standard expansion history

Supports $f(R)$ models as viable alternatives to dark energy

Abstract

The observed accelerated expansion of the Universe at present epoch can be explained by some of the $f(R)$ models without invoking the existence of dark energy or any other such exotic component in cosmic fluid. The $f(R)$ models in Palatini formalism is relatively less explored in recent times with respect to their counterpart in metric formalism. We study seven $f(R)$ models in Palatini formalism: Hu-Sawicki (two cases), Starobinsky, exponential, Tsujikawa, $f(R) = R -\beta /R^ n$, and $f(R)= R + \alpha \ln(R) - \beta$. Following standard statistical procedure and utilizing data sets: type Ia supernovae data, cosmic chronometer observations, baryonic acoustic oscillations data, data from H \textsc{ii} starburst galaxies, local measurements of the \emph{Hubble} parameter ($H_{0}$), and distance priors of cosmic microwave background radiation data, we obtain constraints on the model parameters. When compared with the standard `lambda-cold dark matter model', for many data set combinations, the support for $f(R)$ models is significant. We obtain the relevant quantities for characterizing the accelerated expansion of the Universe, and these quantities are consistent with those obtained in a model-independent way by others. The curve of effective/total equation-of-state parameter, obtained from parameter constraints, clearly shows correct phases of the expansion history: the radiation-dominated epochs and the matter-dominated epochs, of the past, and the current accelerated expansion epoch eventually evolving to de-Sitter phase in the distant future. Overall, our results advocate in favour of pursuing $f(R)$ models in Palatini formalism as a potential alternative for explaining accelerated expansion of the Universe.